Do you have to give your employer your user name and password if you believe they want to log in as you to spy on other employees?

You should not. But it's all depend upon to you. Because if you have love, full trust and blind believe on your dedicate employe, that's the different thing. ;) If the employer owns the operating system and database, he has every right to monitor other employees, and the right to revoke the user access in case of termination of employment. Also to protect the security of his system.